Mobile wireless sensor networks (MWSNs) are a new type of WSN where sink or sensor nodes are mobile. Compared to static WSNs, MWSNs provide many advantages, but the mobility introduces a new security problem of frequent reauthentication. To resolve this problem, several efficient mobile node reauthentication schemes have been proposed. However, they do not work properly in the situation where the mobile node moves between non-neighboring cluster heads. Otherwise, the communication or computation overheads of the mobile node are too high. In this paper, we propose an efficient and practical mobile node reauthentication scheme. In our scheme, through the handover candidate discovery, the mobile node can be reauthenticated efficiently even if it moves between non-neighboring cluster heads. The security analysis shows that our scheme meets the security requirements well and provides better robustness against node compromise attack than the previous study. The performance evaluation shows that our scheme consumes less energy and provides shorter reauthentication delay than previous studies.